Use the Influence Helper to soft select vertices and apply proximity-based falloffs to effects.
Create panel >
(Helpers) > Standard > Object Type rollout > Influence button
Influence Helper shown selecting vertices to create an effect used in an animation of a cartoon train. The inner gizmo is applying maximum influence to all vertices inside while the outer gizmo gradually tapers the effect off.

Enables the helper's effect.
Sets the starting distance of the effect. Click the color swatch to select a new color for the associated gizmo, if desired.
Displays the Near gizmo in the viewport.
Sets the farthest distance of the effect. Click the color swatch to select a new color for the associated gizmo, if desired.
Displays the Far gizmo in the viewport.
Sets the type of falloff curve: either Linear, Smooth or Smoother.
Inverts the falloff value.
Applies a bias amount to the falloff curve.
Sets the amount of bias to apply to the falloff curve.
When enabled, only applies the bias to targets that fall within the selection area.